A377534 Expansion of e.g.f. 1/(1 - x * exp(x^2))^3.

1, 3, 12, 78, 648, 6300, 72000, 939960, 13749120, 223035120, 3969907200, 76890733920, 1609732776960, 36214043785920, 871131980759040, 22310233170825600, 606026217929932800, 17401756135956192000, 526641334386809241600, 16753142420507766873600

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(n-2*k+2,2)/k!.

a(n) ~ n! * n^2 * 2^(n/2 - 1) / ((1 + LambertW(2))^3 * LambertW(2)^(n/2)). - Vaclav Kotesovec, Oct 31 2024

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(n-2*k+2, 2)/k!);

Crossrefs

Cf. A358064, A377533.

Sequence in context: A121421 A349884 A108043 * A058561 A058107 A213139

Adjacent sequences: A377531 A377532 A377533 * A377535 A377537 A377538

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 31 2024

Status

approved